A road or street which is a continuation of a secondary road within a city and which the county board desires to improve, may by resolution of the county board and concurrence by the council of the city be improved as a secondary road assessment district project or part of a project as provided in this chapter. The lands within the city abutting on or adjacent to the street or road may be included within the secondary road assessment district and assessed for the improvement upon the same basis and in the same manner as though the lands were located outside of a city.